In recent years, in a field of mobile communications, Direct Sequence Spread Spectrum (DS-SS) systems such as Code Division Multiple Access (CDMA) systems and Wideband-CDMA (W-CDMA) systems are widely used. However, OFDM systems are more efficient than DS-SS systems from a point of view of frequency utilization efficiency. For this reason, OFDM systems are successively adopted for large-volume data communication systems. The followings are brief descriptions of a basic composition of the OFDM system.
FIG. 7 is a diagram showing fundamental composition of a communication system of the OFDM system. A transmitting device 51 includes an inverse Fast Fourier transformer (IFFT), an orthogonal modulator 2, a local oscillator 3, and an amplifier 4.
In addition, a receiving device 52 includes an amplifier 7, an orthogonal demodulator 8, a local oscillator 9, and a Fast Fourier transformer (FFT). And the communication system indicated in FIG. 7 transmits a signal using in total 2n sub-carriers included in #(1−n) to #(n).
In the transmitting device 51, modulated signals s1−n(t), s2−n(t), s3−n(t), . . . , s−1(t), s0(t), s1(t), . . . , sn(t) corresponding to 2n sub-carriers respectively are inputted to the inverse Fast Fourier transformer (IFFT) 1 and are executed inverse Fourier transform. Through the stated process, a baseband OFDM signal is created. This baseband OFDM signal can be expressed by an equation (1).
                              F          ⁡                      (            t            )                          =                              ∑                          i              =                              1                -                n                                      n                    ⁢                                                                      s                  i                                ⁡                                  (                  t                  )                                            ·              exp                        ⁢                                                  ⁢                          j              ⁡                              (                                  i                  ⁢                                                                          ⁢                                      ω                    o                                    ⁢                  t                                )                                                                        (        1        )            
Here, ω0 is an angular frequency representing sub-carrier interval.
The orthogonal modulator 2 complex-multiplies the baseband OFDM signal by a transmitted local signal from the local oscillator 3. The transmitted local signal can be expressed by an equation (2).L1(t)=exp j{ωct+φ(t)}  (2)
Here, ωc is a carrier angular frequency and φ(t) is a phase noise of the transmitted local signal.
An OFDM signal at the Radio Frequency (RF) band after it was complex-multiplied and generated by the orthogonal modulator 2 can be expressed by the following equation (3) using the above-mentioned equations (1) and (2).
                              O          ⁡                      (            t            )                          =                                            F              ⁡                              (                t                )                                      ·                                          L                1                            ⁡                              (                t                )                                              =                                    ∑                              i                =                                  1                  -                  n                                            n                        ⁢                                                                                s                    i                                    ⁡                                      (                    t                    )                                                  ·                exp                            ⁢                                                          ⁢              j              ⁢                              {                                                                            (                                                                        i                          ⁢                                                                                                          ⁢                                                      ω                            o                                                                          +                                                  ω                          c                                                                    )                                        ⁢                    t                                    +                                      ϕ                    ⁡                                          (                      t                      )                                                                      }                                                                        (        3        )            
The transmitting device 51 amplifies the RF band OFDM signal expressed in the equation (3) in the amplifier 4. The antenna 5 transmits the signal amplified in the amplifier 4. Although high pass filters and others are included in the RF circuits, these descriptions are omitted in FIG. 7.
The receiving device 52 amplifies a signal received by the antenna 6 in the amplifier 7. Then, the orthogonal demodulator 8 complex-multiplies the received signal amplified in the amplifier 7 by a received local signal which is expressed by the following equation (4) that the local oscillator 9 outputs.L2(t)=exp [−j{(ωc−Δω)t−θ(t)}]  (4)
Here, ωc is a carrier angular frequency and θ(t) is a phase noise of the received local signal.
The demodulated OFDM signal obtained by the orthogonal demodulator 8 is expressed by the following equation (5) from the equations (3) and (4).
                                          F            2                    ⁡                      (            t            )                          =                              A            ·                          O              ⁡                              (                t                )                                      ·                                          L                2                            ⁡                              (                t                )                                              =                      A            ⁢                                          ∑                                  i                  =                                      1                    -                    n                                                  n                            ⁢                                                                                          s                      i                                        ⁡                                          (                      t                      )                                                        ·                  exp                                ⁢                                                                  ⁢                j                ⁢                                  {                                                                                                                                                                        (                                                                                                i                                  ⁢                                                                                                                                          ⁢                                                                      ω                                    o                                                                                                  +                                Δω                                                            )                                                        ⁢                            t                                                    +                                                                                                                                                                                          ϕ                            ⁢                                                          (                              t                              )                                                                                +                                                      θ                            ⁡                                                          (                              t                              )                                                                                                                                                            }                                                                                        (        5        )            
Here, “A” is an amplification degree of a transmission path.
The Fourier transformer 10 executes Fourier transform to the demodulated OFDM signal. Then, the Fourier transformer 10 outputs demodulated signals r1−n(t), r2−n(t), r3−n(t), . . . , rn(t) corresponding to 2n sub-carriers respectively. Demodulated signal ri(t) is expressed by the following equation (6), where i=1−n, 2−n, . . . , n.ri(t)=A·si(t)·exp j{Δωt+φ(t)+θ(t)}  (6)
As indicated in the equation (6), the demodulated OFDM signal includes a frequency drift Δω and a phase noise φ(t)+θ(t).
This situation is shown in FIG. 8. FIG. 8 is a diagram showing spectrums of the modulated signal both in the transmitting device and in the receiving device. FIG. 8(A) is a diagram showing a spectrum of 2n modulated signals in the transmitting device. In addition, FIG. 8(B) is a diagram showing a spectrum of the demodulated signals in the receiving device. Corresponding to the modulated signals s1−n(t), s2−n(t), s3−n(t), . . . , sn(t) in the transmitting device, the demodulated signals r1−n(t), r2−n(t), r3−n(t), . . . , rn(t) in the receiving device include the frequency drift Δω and the phase noise φ(t)+θ(t).
As is well-known, interval of frequencies between sub-carriers are very narrow in the OFDM system, and is ranging from kHz to tens-kHz.
For this reason, the OFDM system has a problem that the system is easily affected by influences of the frequency drifts and the phase noises. Accordingly, the various technologies are proposed for settling the problem. For example, an OFDM receiving method disclosed in Japanese Patent Application Laid-Open No. 2001-94525 proposed to calculate drift of a sampling time τ and a phase shift θ from plurality set of two pilot carriers and compensate the sampling time and the phase of all sub-carriers based on the calculated τ and θ. And the OFDM receiving method disclosed in the document further calculates τ and θ from plurality of compensated sub-carriers and once again compensates all compensated sub-carriers.